A geometry problem by Miraj Shah

Geometry Level 4

\[\large \displaystyle \sum_{r=0}^{n} \dbinom nr a^r b^{n-r} \cos[rB-(n-r)A] \]

Let \(a,b\) and \(c\) denote the sides of a triangle and \(A,B,C\) the corresponding angles. Find the closed form of the summation above.

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